YES

Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200)

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## Round 1:
  ## DP problem: 
  Dependency pairs = [dx^#(plus(_0,_1)) -> dx^#(_0), dx^#(plus(_0,_1)) -> dx^#(_1), dx^#(times(_0,_1)) -> dx^#(_0), dx^#(times(_0,_1)) -> dx^#(_1), dx^#(minus(_0,_1)) -> dx^#(_0), dx^#(minus(_0,_1)) -> dx^#(_1), dx^#(neg(_0)) -> dx^#(_0), dx^#(div(_0,_1)) -> dx^#(_0), dx^#(div(_0,_1)) -> dx^#(_1), dx^#(ln(_0)) -> dx^#(_0), dx^#(exp(_0,_1)) -> dx^#(_0), dx^#(exp(_0,_1)) -> dx^#(_1)]
  TRS = {dx(_0) -> one, dx(a) -> zero, dx(plus(_0,_1)) -> plus(dx(_0),dx(_1)), dx(times(_0,_1)) -> plus(times(_1,dx(_0)),times(_0,dx(_1))), dx(minus(_0,_1)) -> minus(dx(_0),dx(_1)), dx(neg(_0)) -> neg(dx(_0)), dx(div(_0,_1)) -> minus(div(dx(_0),_1),times(_0,div(dx(_1),exp(_1,two)))), dx(ln(_0)) -> div(dx(_0),_0), dx(exp(_0,_1)) -> plus(times(_1,times(exp(_0,minus(_1,one)),dx(_0))),times(exp(_0,_1),times(ln(_0),dx(_1))))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.

** END proof description **

Proof stopped at iteration 0
Number of unfolded rules generated by this proof = 0
Number of unfolded rules generated by all the parallel proofs = 0